A kernel approximation to the kriging predictor of a spatial process

✍ Scribed by Michael L. Stein

• Publisher: Springer Japan
• Year: 1991
• Tongue: English
• Weight: 762 KB
• Volume: 43
• Category: Article
• ISSN: 0020-3157
• DOI: 10.1007/bf00116469

✦ Synopsis

Suppose a two-dimensional spatial process z(x) with generalized covariance function G(x, x') c( Ixx'l 2 log Ix -x' I (Matheron, 1973, Adv. in Appl. Probab., 5, 439-468) is observed with error at a number of locations. This paper gives a kernel approximation to the optimal linear predictor, or kriging predictor, of z(x) under this model as the observations get increasingly dense. The approximation is in terms of a Kelvin function which itself can be easily approximated by series expansions. This generalized covariance function is of particular interest because the predictions it yields are identical to an order 2 thin plate smoothing spline. For moderate sample sizes, the kernel approximation is seen to work very well when the observations are on a square grid and fairly well when the observations come from a uniform random sample.